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Physical Review A

Stark splitting of a three-level atom in circularly polarized light

Gao-Jian Zeng

Published Apr 16, 2001• 4 citations
Publisher

Abstract

In this paper, we study Stark splitting of a three-level atom in a circularly polarized electromagnetic wave. We calculate energies of splitting levels. Under some special tuning ways and approximation conditions, these energies have simpler forms and display the following general picture of Stark splitting: the levels of a $\ensuremath{\Lambda}$- or V-type atom are split into six sublevels, while that of a $\ensuremath{\Sigma}$-type atom is split into nine sublevels. We discuss also the occupation probabilities of splitting levels; they are dependent on initial condition. Under the same tuning ways and approximation conditions, some of them may become zero. Therefore under different initial conditions, practical pictures of Stark splitting are not the same. For example, if the atom is initially in its state 1, the practical picture of Stark splitting is the following: the levels of a $\ensuremath{\Lambda}$- or V-type atom are split into four sublevels; that of a $\ensuremath{\Sigma}$-type atom is split into six sublevels. If the atom is initially in its state 2, the practical picture of Stark splitting is the following: the levels of a $\ensuremath{\Lambda}$- or V-type atom are split into five sublevels, while that of a $\ensuremath{\Sigma}$-type atom is split into eight sublevels.

DOI
10.1103/physreva.63.053408

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In this paper, we study Stark splitting of a three-level atom in a circularly polarized electromagnetic wave. We calculate energies of splitting levels. Under some special tuning ways and approximation conditions, these energies have simpler forms and display the following general picture of Stark splitting: the levels of a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ- or V-type atom are split into six sublevels, while that of a \ensuremathΣ\ensuremath{\Sigma}\ensuremathΣ-type atom is split into nine sublevels. We discuss also the occupation probabilities of splitting levels; they are dependent on initial condition. Under the same tuning ways and approximation conditions, some of them may become zero. Therefore under different initial conditions, practical pictures of Stark splitting are not the same. For example, if the atom is initially in its state 1, the practical picture of Stark splitting is the following: the levels of a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ- or V-type atom are split into four sublevels; that of a \ensuremathΣ\ensuremath{\Sigma}\ensuremathΣ-type atom is split into six sublevels. If the atom is initially in its state 2, the practical picture of Stark splitting is the following: the levels of a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ- or V-type atom are split into five sublevels, while that of a \ensuremathΣ\ensuremath{\Sigma}\ensuremathΣ-type atom is split into eight sublevels.
The propagation of strongly polarized electromagnetic waves through a resonance medium, with arbitrary angular momenta of the levels, is investigated in the adiabatic-following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarized wave are constructed and the picture of the shift of energy level splittings is discussed. Exact formulae for the nonlinear refractive index of the medium in the field of the circularly (linearly) polarized wave are found. The propagation of counterpropagating polarized waves—an intense pump wave and a probe light signal—through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced rotation of the plane of polarization for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
In this paper, we study the behavior of a two-level atom in an electromagnetic wave of circular polarization. A general solution to the Schr\"odinger equation is obtained, and the action of the electromagnetic wave on the atom is analyzed in detail. It is shown that the levels of the atom would be split, with the energy difference between the split levels the same for the two states of the atom. The atom would acquire an average momentum, with its direction the same as the propagating direction of the electromagnetic wave, showing the expelling action of the electromagnetic wave on the atom; or with its direction opposite to the propagating direction of the electromagnetic wave, showing the trapping action of the electromagnetic wave on the atom. The properties of the action are dependent on the initial state of the atom. The average expelling and trapping forces exerted on the atom by the electromagnetic wave are determined. Two cases of ``resonance'' and ``strict detuning'' are discussed particularly. Under the resonance case, the transition probability reaches its maximum for a given time. In the strict detuning case, the atom is not influenced by the electromagnetic wave.
The propagation of a strongly polarised electromagnetic wave through a resonance medium with arbitrary angular momenta of the levels is investigated in the adiabatic following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarised wave are constructed and the picture of the energetic level splitting and shift is discussed. Exact formulae for the non-linear refractive index of the medium in the field of the circularly (linearly) polarised wave are found. The propagation of counterpropagating polarised waves-an intense pump wave and a probe light signal-through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced pump angle of rotation of the ellipse (plane) of polarisation for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
Based on this solution for Schrǒdinger equation, the atom lifetime in an electromagnetic wave of circular polarization is studied. When the frequency of a circularly polarized electromagnetic wave is equal to the atomic frequency, the atom lifetime of tow level atom is not influenced by the electromagnetic wave. For a ∧ type three level atom in a circularly polarized electromagnetic wave, we modulate the frequency of the electromagnetic wave to study the atom lifetime and show that the approximate condition in this paper is rational.